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Proof step 127 from proof shiftright-rec-8-neg (previous step)

2 ≠ 0 ∧ 256 ≠ 0, (i0 - 1) >> (j - 1) = ((i0 - 1) / 256 - 1) >> (j - 9), i0 < j, i0 ≤ 0, 0 < j, 8 < j, ∀ i, j0. i→n(j0) < i→n(j) → 8 ≤ j0 ∧ i < 0 ∧ 0 < j0 ∧ 0 ≤ j0 → i >> j0 = (i - 255) / 256 >> (j0 - 8) ⊦ j = 0, (i0 - 1) / 256 = ((i0 * 2 - 1) / 2) / 256, (i0 * 2 - 1) % 256 = 0, j = 8, (i0 - 1) % 256 = 0, (i0 - 1) >> (j - 1) = (((i0 * 2 - 1) / 2) / 256 - 1) >> (j - 9)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i < 0 ∧ i % 2 = 0 → (i - 1) / 2 = i / 2 subst: [i] → [i0 * 2] rotate: F spec: int-div inst: name: div-twoodd-01

Additional information

Used simplifier rules: j ≠ 0, j0 ≠ 0 ⊦ (i / (* j)) / (* j0) = i / (j * j0);% ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ (i * 2) % 2 = 0; Used terms: i0 * 2